Reconstruction technique for off-axis electron holography using coarse fringes

A reconstruction technique for off-axis electron holography not requiring Fourier transformation is presented. Background intensity and amplitude modulation recorded in a hologram are normalized using an envelope function, and a cosine-function image corresponding to interference fringes is retrieved from the hologram. A reconstructed phase image is then calculated from the retrieved cosine image. After phase unwrapping, the phases due to carrier frequency and Fresnel diffraction from the biprism are removed using a reference hologram, and the corrected phase image is obtained. One advantage of this method is that the spatial resolution does not rely on the interference fringe spacing. Another advantage is that the phase image has no artifacts due to windowing of the sideband, which occurs in the usual Fourier-transformation method. Details of the calculation process and demonstrations of the method using a latex sphere particle and self-assembled Co nanoparticles are described.     

Observation of surfaces by reflection electron holography.

Reflection electron holography is described as a method to observe sub-A surface morphology. Phase shift of a Bragg-reflected electron wave was measured by means of holographic interferometry using an electron microscope equipped with a field emission electron gun and an electron biprism. A short wavelength of high energy electrons is the essential key to the high vertical sensitivity of this method, since geometrical path differences produced by the surface topography are measured in units of wavelengths in interferometrical measuring. Phase shift at a monoatomic step and the displacement field around a dislocation emerging on the surface were observed.     

Diffracted phase and amplitude measurements by energy-filtered convergent-beam holography (CHEF)

Interference between transmitted and diffracted disks in convergent-beam electron diffraction (CBED) patterns using the CBED+EBI method proposed by Herring et al. is explored using different optical configurations on a spherical aberration corrected transmission electron microscope equipped with a biprism and imaging energy filter: the SACTEM-Toulouse. We will relate the amplitude and phase of these interference patterns, which we call convergent-beam holography (CHEF), to microscope transfer theory and the complex amplitudes of the diffracted beams. Experimental CHEF patterns recorded in the absence of aberration correction will be compared with simulations to validate the theory concerning the effect of microscope aberrations and current instabilities. Then, using aberration correction, we propose a scheme for eliminating the effect of the microscope, so that the diffracted amplitudes and phase due to dynamical scattering within the specimen can be studied. Experimental results are compared with simulations performed using the full dynamical theory. The potential for studying diffracted amplitudes and phases using CHEF analysis is discussed.     

Amplitude division electron interferometry

The lattice fringes produced by a single crystal placed in the normal specimen level are modulated by a specimen (phase object) located at the level of the diffraction aperture of a high resolution electron microscope. The advantages of this amplitude division interferometer compared with a microscope equipped with an electrostatic biprism are higher intensities, as extended sources can be used, and larger interference field.     

Energy-filtered electron-diffracted beam holography

A method of energy-filtered electron holography is described where any two electron-diffracted beams can be interfered using an electron biprism. A Gatan image filter is used to select the energy loss of the electrons produced in the holograms. Gallium arsenide is used as the TEM specimen. This method of microscopy confirms that fringes extending beyond a limiting aperture were due to inelastically scattered electrons and specifically electrons scattered from the bulk plasmon. The degree of coherence of the zero-loss and energy-loss electrons were high and measured to be approximately 0.3, which was maintained even for the high energy-loss electrons up to 100 eV. Future systematic studies using this method should help understand the Stobbs factor and contribute to the development of quantitative high-resolution electron microscopy.     

Calculation of phase changes of electron waves near excited nanoparticles

When a metallic nanoparticle is illuminated by electromagnetic radiation of the appropriate frequency, strong electric and magnetic fields are generated close to the surface of the particle by the valence electrons of the metal. The energy in these surface excitations can be transferred to external electrons passing near the particle (energy-gain spectral spectroscopy) and they change the phase of the zero-loss component of the electron wave. This paper provides an estimate of how the phase of the wave at the image plane of a 100-kV transmission electron microscope varies with position in the image plane. For a 16-nm radius gold sphere illuminated by the light of wavelength 500 nm and irradiance 10 MW/cm², the phase in the image plane changes by 0.002 rad/nm along a radial line outside the sphere. Changes of similar magnitude have been measured in previous studies.     

Theoretical aspects of image formation in the aberration-corrected electron microscope

The theoretical aspects of image formation in the transmission electron microscope (TEM) are outlined and revisited in detail by taking into account the elastic and inelastic scattering. In particular, the connection between the exit wave and the scattering amplitude is formulated for non-isoplanatic conditions. Different imaging modes are investigated by utilizing the scattering amplitude and employing the generalized optical theorem. A novel obstruction-free anamorphotic phase shifter is proposed which enables one to shift the phase of the scattered wave by an arbitrary amount over a large range of spatial frequencies. In the optimum case, the phase of the scattered wave and the introduced phase shift add up to −π/2 giving negative contrast. We obtain these optimum imaging conditions by employing an aberration-corrected electron microscope operating at voltages below the knock-on threshold for atom displacement and by shifting optimally the phase of the scattered electron wave. The optimum phase shift is achieved by adjusting appropriately the constant phase shift of the phase plate and the phase shift resulting from the defocus and the spherical aberration of the corrected objective lens. The realization of this imaging mode is the aim of the SALVE project (Sub-Å Low-Voltage Electron microscope).     

Inelastic electron holography

Coherence of inelastically scattered electrons was investigated by means of biprism interference experiments performed in a transmission electron microscope equipped with a highly coherent field emission gun and an imaging filter. The experimental results show that within the wave inelastically scattered at aluminium plasmons there is in fact an area of about 10 nm diameter with coherence sufficient to take electron holograms.     

Quantitative phase-sensitive imaging in a transmission electron microscope

This paper presents a new technique for forming quantitative phase and amplitude electron images applicable to a conventional transmission electron microscope. With magnetised cobalt microstructures used as a test object, we use electron holography to obtain an independent measurement of the phase shift. After a suitable calibration of the microscope, we obtain quantitative agreement of the phase shift imposed on the 200 keV electrons passing through the sample.     

Object wave reconstruction by phase-plate transmission electron microscopy

A method is described for the reconstruction of the amplitude and phase of the object exit wave function by phase-plate transmission electron microscopy. The proposed method can be considered as in-line holography and requires three images, taken with different phase shifts between undiffracted and diffracted electrons induced by a suitable phase-shifting device. The proposed method is applicable for arbitrary object exit wave functions and non-linear image formation. Verification of the method is performed for examples of a simulated crystalline object wave function and a wave function acquired with off-axis holography. The impact of noise on the reconstruction of the wave function is investigated.     

Improved Zernike‐type phase contrast for transmission electron microscopy

Zernike phase contrast has been recognized as a means of recording high‐resolution images with high contrast using a transmission electron microscope. This imaging mode can be used to image typical phase objects such as unstained biological molecules or cryosections of biological tissue. According to the original proposal discussed in Danev and Nagayama (2001) and references therein, the Zernike phase plate applies a phase shift of π/2 to all scattered electron beams outside a given scattering angle and an image is recorded at Gaussian focus or slight underfocus (below Scherzer defocus). Alternatively, a phase shift of ‐π/2 is applied to the central beam using the Boersch phase plate. The resulting image will have an almost perfect contrast transfer function (close to 1) from a given lowest spatial frequency up to a maximum resolution determined by the wave length, the amount of defocus and the spherical aberration of the microscope. In this paper, I present theory and simulations showing that this maximum spatial frequency can be increased considerably without loss of contrast by using a Zernike or Boersch phase plate that leads to a phase shift between scattered and unscattered electrons of only π /4, and recording images at Scherzer defocus. The maximum resolution can be improved even more by imaging at extended Scherzer defocus, though at the cost of contrast loss at lower spatial frequencies.     

A twin-wave quadrature interferometer for diagnostics of pulsed processes in hydrogen and erosion plasma

A two-wave interferometer is described that is based on 0.6328-and 3.3922-μm He-Ne lasers and allows separation of the contributions of free electrons and the neutral component in partially ionized plasma to the phase shift of a probing electromagnetic wave under conditions of possible vibrations of the facility’s optical elements. Using the quadrature method for forming informative signals, phase shifts were measured in a wide range of fractions of an interference fringe to several fringes with a high homogeneous differential sensitivity. The interferometer was used to measure the dynamics of the linear electron density of both an atmospheric-pressure erosion capillary discharge in air and plasma of a hydrogen target in experiments on deceleration of heavy ions in an ionized substance.     

基于全息图放大的数字全息显微结构测量

针对典型预放大数字显微全息光路中存在的二次位相误差,本文设计了基于全息图放大的数字全息显微光路。此设计中,光束首先照射透明显微物体,然后与平行参考光干涉,形成全息图,最后经显微镜获得放大的全息图。这种光路从系统上直接消除了主要由球面波引起的位相畸变,有利于数字处理及实时化。作者以位相光栅(30 lines/mm,槽深约0.3 µm)作为实验样本,对此光路进行了分析研究,并分别用菲涅耳近似法和卷积法再现单幅全息图,同时获取了物体的强度信息和三维位相信息,位相深度的计算结果为0.27 µm。结果表明本文设计的光路对二次位相产生的离焦误差有明显的抑制作用。     

The tuning of a Zernike phase plate with defocus and variable spherical aberration and its use in HRTEM imaging

With the advent of the double-hexapole aberration corrector in transmission electron microscopy the spherical aberration of the imaging system has become a tunable imaging parameter like the objective lens defocus. Now Zernike phase plates, altering the phase of the diffracted electron wave, can be approximated more perfectly than with the lens defocus alone, and the amount of phase change can be adjusted within wide limits. The tuning of the phase change allows an optimum contrast transfer in high-resolution imaging even for thick crystalline objects, thus surpassing the limits of the well-known Scherzer lamda/4 phase plate to the imaging of thin objects. The optimum values for the spherical aberration and the lens defocus are derived, and the limits and imperfections of the approximation explored. A mathematical link to the channelling approximation of high-energy electron diffraction shows how the image contrast of atomic columns can be improved systematically within wide thickness limits. Depending on the specimen thickness different combinations of spherical aberration and defocus are favourable: positive spherical aberration with an underfocus, zero spherical aberration with zero defocus, as well as negative spherical aberration with an overfocus.     

The Fresnel effect of a defocused biprism on the fringes in inelastic holography

We present energy filtered holography experiments on a thin foil of Al. By propagating the reduced density matrix of the probe electron through the microscope, we quantitatively predict the fringe contrast as a function of energy loss. Fringe contrast simulations include the effect of Fresnel fringes created at the edges of the defocused biprism, the effect of partial coherence in combination with inelastic scattering, and the effect of a finite energy distribution of the incoming beam.     

Quantitative analysis of image contrast in phase contrast STEM for low dose imaging

This work quantitatively evaluates the contrast in phase contrast images of thin vermiculite crystals recorded by TEM and aberration-corrected bright-field STEM. Specimen movement induced by electron irradiation remains a major problem limiting the phase contrast in TEM images of radiation-sensitive specimens. While spot scanning improves the contrast, it does not eliminate the problem. One possibility is to utilise aberration-corrected scanning transmission electron microscopy (STEM) with an Ångstrom-sized probe to illuminate the sample, and thus further reduce irradiation-induced specimen movement. Vermiculite is relatively radiation insensitive in TEM to electron fluences below 100,000 e⁻/Ų and this is likely to be similar for STEM although different damage mechanisms could occur. We compare the performance of a TEM with a thermally assisted field emission electron gun (FEG) and charge coupled device (CCD) image capture to the performance of STEMs with spherical aberration correction, cold field emission electron sources and photomultiplier tube image capture at a range of electron fluences and similar illumination areas. We show that the absolute contrast of the phase contrast images obtained by aberration-corrected STEM is better than that obtained by TEM. Although the STEM contrast is higher, the efficiency of collection of electrons in bright field STEM is still much less than that in bright field TEM (where for thin samples virtually all the electrons contribute to the image), and the SNR of equivalent STEM images is three times lower. This is better than expected, probably due to the absence of a frequency dependent modulation transfer function in the STEM detection system. With optimisation of the STEM bright field collection angles, the efficiency may approach that of bright field TEM, and if reductions in beam-induced specimen movement are found, STEM could surpass the overall performance of TEM.     

Computer simulation of Lorentz electron micrographs of thin magnetic particles

Lorentz electron microscopy is a powerful tool for high-resolution studies of magnetic structures, not only in continuous thin films, but also in spatially limited, i.e. individual particles. In addition to the experimental studies of magnetic particulate media it is interesting to simulate images in order to compare them with experimental results, as it is practiced in high-resolution electron microscopy. This paper introduces a software package which simulates the Lorentz microscopical image of magnetic structures in thin particles. While other simulation programs deal with infinite magnetic films with homogeneous thickness, the major difference in our calculation is that we take into account the finite dimensions of the particle for specimens of various sizes and shapes. That means the phase shift due to the inner potential depending on the geometrical shape of a magnetic particle is added to the phase shift depending on its magnetic microstructure. The following article presents the computation methods and its results and compares it with experimental findings.